Finite Group Databasebeta

← C2×#10595022 #11900457

Subgroups — C2×#10595022 #11900457

Order 1152.

3925 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C23×C3×C4×D3C211yesmaximal, characteristic, complemented
3C2×#64135C211yesmaximal, characteristic, complemented
4C2×#63976C212yesmaximal, complemented
5C2×#63961C212yesmaximal, complemented
6#10595022C2116yesmaximal, direct product factor
7C2×#63908C212yesmaximal, complemented
8C2×C4×#625C214yesmaximal, complemented
9C2×#63856C212yesmaximal, complemented
10C2×#5828—31nomaximal
11C2×#5791—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C22×C3×#67C2212yes—
15C23×C3×Dic3C2211yescharacteristic
16C2×C3×#235—28no—
17C2×C3×#235C2218yescomplemented
18C22×C3×D12C2211yescharacteristic, complemented
19C22×C3×C4×D3—28no—
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2212yes—
22C22×C3×C4×D3C2218yescomplemented
23C22×C3×C4×D3C2212yescomplemented
24C22×C3×Dic6C2211yescharacteristic, complemented
25C22×#625C2214yes—
26C2×#3757C2212yes—
27#64135C2218yescomplemented
28C2×C4⋊(C3⋊Dic3)C2212yescomplemented
29C2×C4×C3⋊Dic3C2212yescomplemented
30#63976C22116yescomplemented
31C2×#3724C2214yescomplemented
32#63961C22116yescomplemented
33C2×(C2×D3)⋊Dic3C2214yes—
34C2×(C2×D3)⋊Dic3C2214yescomplemented
35#63908C22116yescomplemented
36C4×#625C22132yescomplemented
37#63856C22116yescomplemented
38C22×C3×#41—31no—
39C24×C3×C4—31no—
40C22×#235D311yescharacteristic, complemented
41C23×C4×D3D311yescharacteristic, complemented
42C2×#953—32no—
43#5828—316no—
44C2×#946—32no—
45C2×#938—32no—
46C2×#937—32no—
47C2×#935—32no—
48#5791—316no—
49C2×#930—32no—
50C2×#929—32no—
51C2×C4×#67—34no—
52C2×C4×#67—34no—
53C2×#926—31no—
54C2×#926—31no—
55C2×#926—61no—
56C2×#924—32no—
57C24×C32C2311yescharacteristic
58C23×C3×D3—24no—
59C23×C3×D3—28no—
60C23×C3×D3C2312yes—
61C23×C3×D3C2314yes—
62C23×C3×D3C2312yes—
63C22×C32×C4D418yescomplemented
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2314yes—
67C22×C3⋊Dic3C2314yes—
68C2×C3×#67—28no—
69C2×C3×#67C2318yes—
70C22×C3×Dic3—24no—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2314yes—
74C3×#235—232no—
75C2×C3×D12—24no—
76C2×C3×D12C2314yescomplemented
77C2×C3×C4×D3—28no—
78C2×C3×C4×D3—28no—
79C2×C3×C4×D3—28no—
80C2×C3×C4×D3—232no—
81C2×C3×C4×D3C2318yes—
82C2×C3×C4×D3C2318yes—
83C2×C3×C4×D3C2318yescomplemented
84C2×C3×Dic6—24no—
85C2×C3×Dic6C2314yescomplemented
86C2×#625—216no—
87C2×#625C23116yes—
88#3757C2318yes—
89C4⋊(C3⋊Dic3)C2318yescomplemented
90C4×C3⋊Dic3C2318yescomplemented
91#3724C23116yescomplemented
92(C2×D3)⋊Dic3C23116yes—
93(C2×D3)⋊Dic3C23116yescomplemented
94C2×#525—91noSylow
95C25×C3—31no—
96C24×D3C2×D311yescharacteristic
97C2×C3×#41—38no—
98C2×C3×#41—68no—
99C22×C3×Q8—31no—
100C22×C3×D4—32no—
101C22×C3×D4—31no—
102C23×C3×C4—21no—
103C23×C3×C4—31no—
104C23×C3×C4—32no—
105C23×C3×C4—32no—
106C23×C3×C4—38no—
107C23×C3×C4—32no—
108C23×C3×C4—68no—
109C23×C3×C4C2×D311yescharacteristic
110C23×C3×C4C2×D311yescharacteristic
111C22×#67—34no—
112C22×#67—34no—
113C22×#67C2×D312yes—
114C23×Dic3C2×D311yescharacteristic
115C2×#235—28no—
116C2×#235C2×D318yescomplemented
117C22×D12C2×D311yescharacteristic, complemented
118C22×C4×D3—28no—
119C22×C4×D3C2×D312yes—
120C22×C4×D3C2×D312yes—
121C22×C4×D3C2×D318yescomplemented
122C22×C4×D3C2×D312yescomplemented
123C22×Dic6C2×D311yescharacteristic, complemented
124#953—316no—
125C2×#217—32no—
126C2×#217—32no—
127C2×#217—34no—
128C2×#217—34no—
129C2×#217—62no—
130#946—316no—
131#938—316no—
132#937—316no—
133#935—316no—
134#930—316no—
135#929—316no—
136C4×#67—332no—
137C4×#67—332no—
138C2×(C2×D3)⋊C4—34no—
139C2×(C2×D3)⋊C4—34no—
140#926—38no—
141#926—38no—
142#926—68no—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—62no—
146#924—316no—
147C2×Dic3⋊C4—34no—
148C2×Dic3⋊C4—34no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—62no—
152C23×C32—24no—
153C23×C32C2×D414yes—
154C23×C32C2412yes—
155C23×C32C2411yescharacteristic
156C22×C3×D3—232no—
157C22×C3×D3—28no—
158C22×C3×D3—24no—
159C22×C3×D3—24no—
160C22×C3×D3—216no—
161C22×C3×D3—24no—
162C22×C3×D3—28no—
163C22×C3×D3#4118yescomplemented
164C22×C3×D3C2414yes—
165C22×C3×D3C2414yes—
166C2×C32×C4C2×D414yes—
167C2×C32×C4C2×D414yes—
168C2×C32×C4C2×D4116yescomplemented
169C2×C32×C4C2412yes—
170C2×C32×C4C2412yes—
171C2×C3⋊Dic3—28no—
172C2×C3⋊Dic3C2418yes—
173C3×#67—216no—
174C2×C3×Dic3—24no—
175C2×C3×Dic3—28no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3C2414yes—
178C2×C3×Dic3C2414yes—
179C3×D12—28no—
180C3×C4×D3—216no—
181C3×C4×D3—216no—
182C3×C4×D3—216no—
183C3×Dic6—28no—
184#625—232no—
185C22×#41—31no—
186C24×C4—31no—
187#525—916no—
188C2×#123—92no—
189C2×C22⋊Q8—92no—
190C2×#121—92no—
191C2×#120—92no—
192C2×C4×D4—94no—
193C2×#117—91no—
194C24×C3—21no—
195C24×C3—32no—
196C24×C3—34no—
197C24×C3—32no—
198C24×C3—68no—
199C24×C3—64no—
200C24×C3C22×D311yescharacteristic
201C24×C3C22×D311yescharacteristic
202C23×D3—24no—
203C23×D3—28no—
204C23×D3C22×D312yes—
205C23×D3C22×D314yes—
206C23×D3C22×D312yes—
207C3×#41—632no—
208C2×C3×Q8—34no—
209C2×C3×Q8—64no—
210C2×C3×D4—38no—
211C2×C3×D4—34no—
212C2×C3×D4—68no—
213C2×C3×D4—64no—
214C22×C3×C4—28no—
215C22×C3×C4—21no—
216C22×C3×C4—24no—
217C22×C3×C4—21no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—34no—
221C22×C3×C4—38no—
222C22×C3×C4—38no—
223C22×C3×C4—38no—
224C22×C3×C4—64no—
225C22×C3×C4—68no—
226C22×C3×C4—68no—
227C22×C3×C4—68no—
228C22×C3×C4—632no—
229C22×C3×C4#6718yescomplemented
230C22×C3×C4#6718yescomplemented
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D314yes—
234C22×C3×C4C22×D314yes—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—28no—
238C2×#67—316no—
239C2×#67—316no—
240C2×#67—616no—
241C2×#67—616no—
242C2×#67C22×D318yes—
243C22×Dic3—24no—
244C22×Dic3—34no—
245C22×Dic3—34no—
246C22×Dic3—64no—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D314yes—
250#235—232no—
251C2×D12—24no—
252C2×D12C22×D314yescomplemented
253C2×C4×D3—28no—
254C2×C4×D3—28no—
255C2×C4×D3—28no—
256C2×C4×D3—232no—
257C2×C4×D3C22×D318yes—
258C2×C4×D3C22×D318yes—
259C2×C4×D3C22×D318yescomplemented
260C2×Dic6—24no—
261C2×Dic6C22×D314yescomplemented
262#217—38no—
263#217—38no—
264#217—316no—
265#217—316no—
266#217—68no—
267(C2×D3)⋊C4—316no—
268(C2×D3)⋊C4—316no—
269C4⋊Dic3—38no—
270C4⋊Dic3—38no—
271C4⋊Dic3—68no—
272Dic3⋊C4—316no—
273Dic3⋊C4—316no—
274C4×Dic3—38no—
275C4×Dic3—38no—
276C4×Dic3—68no—
277C22×C32—28no—
278C22×C32—24no—
279C22×C32C22×D414yes—
280C22×C32C22×D412yes—
281C22×C32C2×#4114yes—
282C22×C32C2511yescharacteristic
283C2×C3×D3—232no—
284C2×C3×D3—216no—
285C2×C3×D3—24no—
286C2×C3×D3—24no—
287C2×C3×D3—24no—
288C2×C3×D3—28no—
289C2×C3×D3—48no—
290C2×C3×D3C2×#4118yescomplemented
291C32×C4C22×D414yes—
292C32×C4C22×D414yes—
293C3⋊Dic3—28no—
294C3×Dic3—24no—
295C3×Dic3—24no—
296C25—31no—
297C2×#41—38no—
298C2×#41—68no—
299C22×Q8—31no—
300C22×D4—32no—
301C22×D4—31no—
302C22×D4—94no—
303C23×C4—31no—
304C23×C4—32no—
305C23×C4—38no—
306C23×C4—32no—
307C23×C4—32no—
308C23×C4—68no—
309C23×C4D3211yescharacteristic
310#123—916no—
311C22⋊Q8—916no—
312#121—916no—
313#120—916no—
314C4×D4—932no—
315#117—98no—
316C2×C4⋊C4—94no—
317C2×C4⋊C4—92no—
318C2×C22⋊C4—94no—
319C2×C22⋊C4—94no—
320C2×C22⋊C4—92no—
321C2×C42—92no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—21no—
325C23×C3—22no—
326C23×C3—24no—
327C23×C3—38no—
328C23×C3—34no—
329C23×C3—34no—
330C23×C3—44no—
331C23×C3—616no—
332C23×C3—632no—
333C23×C3—64no—
334C23×C3—68no—
335C23×C3—64no—
336C23×C3—68no—
337C23×C3—64no—
338C23×C3C2×#6714yes—
339C23×C3C2×#6714yes—
340C23×C3C23×D312yes—
341C23×C3C23×D312yes—
342C23×C3C23×D311yescharacteristic
343C23×C3C23×D311yescharacteristic
344C22×D3—232no—
345C22×D3—24no—
346C22×D3—28no—
347C22×D3—24no—
348C22×D3—216no—
349C22×D3—28no—
350C22×D3—24no—
351C22×D3#23518yescomplemented
352C22×D3C23×D314yes—
353C22×D3C23×D314yes—
354C3×Q8—68no—
355C3×D4—616no—
356C3×D4—68no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—216no—
362C2×C3×C4—34no—
363C2×C3×C4—34no—
364C2×C3×C4—68no—
365C2×C3×C4—64no—
366C2×C3×C4—64no—
367C2×C3×C4—616no—
368C2×C3×C4—616no—
369C2×C3×C4—616no—
370C2×C3×C4C2×#6714yes—
371C2×C3×C4C2×#6714yes—
372C2×C3×C4C2×#6714yes—
373C2×C3×C4C2×#6714yes—
374C2×C3×C4C2×#67116yescomplemented
375C2×C3×C4C2×#67116yescomplemented
376C2×C3×C4C23×D312yes—
377C2×C3×C4C23×D312yes—
378C2×C3×C4C23×D312yes—
379C2×C3×C4C23×D312yes—
380#67—216no—
381#67—632no—
382#67—632no—
383C2×Dic3—24no—
384C2×Dic3—28no—
385C2×Dic3—24no—
386C2×Dic3—38no—
387C2×Dic3—38no—
388C2×Dic3—68no—
389C2×Dic3—68no—
390C2×Dic3—68no—
391C2×Dic3—128no—
392C2×Dic3C23×D314yes—
393C2×Dic3C23×D314yes—
394D12—28no—
395C4×D3—216no—
396C4×D3—216no—
397C4×D3—216no—
398Dic6—28no—
399C2×C32—24no—
400C2×C32#52514yescomplemented
401C2×C32C23×D411yescharacteristic
402C2×C32C22×#4112yes—
403C3×D3—28no—
404C3×D3—44no—
405C24—32no—
406C24—32no—
407C24—34no—
408C24—68no—
409C24—64no—
410C24C2×D3211yescharacteristic
411#41—632no—
412C2×Q8—34no—
413C2×Q8—64no—
414C2×D4—38no—
415C2×D4—34no—
416C2×D4—68no—
417C2×D4—64no—
418C2×D4—916no—
419C2×D4—1816no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—34no—
423C22×C4—38no—
424C22×C4—38no—
425C22×C4—38no—
426C22×C4—64no—
427C22×C4—68no—
428C22×C4—68no—
429C22×C4—68no—
430C22×C4—632no—
431C22×C4—94no—
432C22×C4#62518yescomplemented
433C22×C4C2×D3211yescharacteristic
434C22×C4C2×D3214yes—
435C22×C4C2×D3211yescharacteristic
436C4⋊C4—916no—
437C4⋊C4—98no—
438C22⋊C4—916no—
439C22⋊C4—916no—
440C22⋊C4—98no—
441C42—98no—
442C22×C3—24no—
443C22×C3—24no—
444C22×C3—28no—
445C22×C3—28no—
446C22×C3—24no—
447C22×C3—22no—
448C22×C3—24no—
449C22×C3—21no—
450C22×C3—38no—
451C22×C3—44no—
452C22×C3—48no—
453C22×C3—632no—
454C22×C3—64no—
455C22×C3—64no—
456C22×C3—616no—
457C22×C3—68no—
458C22×C3—64no—
459C22×C3—128no—
460C22×C3C2×#23514yes—
461C22×C3D3×#4114yes—
462C22×C3C22×#6714yes—
463C22×C3C22×#6714yes—
464C22×C3C22×#6712yes—
465C22×C3C22×#6712yes—
466C22×C3C24×D311yescharacteristic
467C22×C3C24×D311yescharacteristic
468C2×D3—232no—
469C2×D3—24no—
470C2×D3—24no—
471C2×D3—216no—
472C2×D3—28no—
473C2×D3—24no—
474C2×D3—48no—
475C2×D3C2×#23518yescomplemented
476C3×C4—24no—
477C3×C4—24no—
478C3×C4—64no—
479C3×C4—64no—
480C3×C4C22×#6714yes—
481C3×C4C22×#6714yes—
482C3×C4C22×#6714yes—
483C3×C4C22×#6714yes—
484Dic3—24no—
485Dic3—24no—
486Dic3—68no—
487Dic3—68no—
488Dic3—128no—
489C32C2×#52511yescharacteristic, complemented, Sylow
490C23—24no—
491C23—38no—
492C23—34no—
493C23—34no—
494C23—616no—
495C23—632no—
496C23—64no—
497C23—68no—
498C23—64no—
499C23—68no—
500C23—64no—
501C23C2×#62514yes—
502C23C22×D3212yes—
503C23C22×D3211yescharacteristic
504Q8—68no—
505D4—616no—
506D4—68no—
507D4—1832no—
508C2×C4—34no—
509C2×C4—34no—
510C2×C4—68no—
511C2×C4—64no—
512C2×C4—64no—
513C2×C4—616no—
514C2×C4—616no—
515C2×C4—616no—
516C2×C4—98no—
517C2×C4—188no—
518C2×C4C2×#62514yes—
519C2×C4C2×#62514yes—
520C2×C4C2×#625116yescomplemented
521C2×C4C22×D3212yes—
522C2×C4C22×D3212yes—
523C2×C3—24no—
524C2×C3—24no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—24no—
528C2×C3—44no—
529C2×C3—68no—
530C2×C3—124no—
531C2×C3#579114yescomplemented
532C2×C3#582814yescomplemented
533C2×C3C22×#23512yes—
534C2×C3C2×D3×#4112yes—
535C2×C3C23×#6711yescharacteristic
536C2×C3C23×#6711yescharacteristic
537D3—28no—
538D3—44no—
539C22—24no—
540C22—28no—
541C22—38no—
542C22—632no—
543C22—64no—
544C22—64no—
545C22—616no—
546C22—68no—
547C22—64no—
548C22—128no—
549C22D3×#23514yes—
550C22C22×#62514yes—
551C22C22×#62512yes—
552C22C23×D3211yescharacteristic
553C4—64no—
554C4—64no—
555C4—188no—
556C4C22×#62514yes—
557C4C22×#62514yes—
558C3—21no—
559C3C2×#579111yescharacteristic, complemented
560C3C2×#582811yescharacteristic, complemented
561C2—24no—
562C2—68no—
563C2—124no—
564C2#1059502214yesdirect product factor
565C2C2×D3×#23512yes—
566C2C23×#62511yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C23×C3×C4×D3C2semidirect
3. C2×#64135C2semidirect
4. C2×#63976C2semidirect
5. C2×#63961C2semidirect
6. #10595022C2direct (N × H)
7. C2×#63908C2semidirect
8. C2×C4×#625C2semidirect
9. C2×#63856C2semidirect
17. C2×C3×#235C22semidirect
18. C22×C3×D12C22semidirect
22. C22×C3×C4×D3C22semidirect
23. C22×C3×C4×D3C22semidirect
24. C22×C3×Dic6C22semidirect
27. #64135C22semidirect
28. C2×C4⋊(C3⋊Dic3)C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
30. #63976C22semidirect
31. C2×#3724C22semidirect
32. #63961C22semidirect
34. C2×(C2×D3)⋊Dic3C22semidirect
35. #63908C22semidirect
36. C4×#625C22semidirect
37. #63856C22semidirect
40. C22×#235D3semidirect
41. C23×C4×D3D3semidirect
63. C22×C32×C4D4semidirect
76. C2×C3×D12C23semidirect
83. C2×C3×C4×D3C23semidirect
85. C2×C3×Dic6C23semidirect
89. C4⋊(C3⋊Dic3)C23semidirect
90. C4×C3⋊Dic3C23semidirect
91. #3724C23semidirect
93. (C2×D3)⋊Dic3C23semidirect
116. C2×#235C2×D3semidirect
117. C22×D12C2×D3semidirect
121. C22×C4×D3C2×D3semidirect
122. C22×C4×D3C2×D3semidirect
123. C22×Dic6C2×D3semidirect
163. C22×C3×D3#41semidirect
168. C2×C32×C4C2×D4semidirect
229. C22×C3×C4#67semidirect
230. C22×C3×C4#67semidirect
252. C2×D12C22×D3semidirect
259. C2×C4×D3C22×D3semidirect
261. C2×Dic6C22×D3semidirect
290. C2×C3×D3C2×#41semidirect
351. C22×D3#235semidirect
374. C2×C3×C4C2×#67semidirect
375. C2×C3×C4C2×#67semidirect
400. C2×C32#525semidirect
432. C22×C4#625semidirect
475. C2×D3C2×#235semidirect
489. C32C2×#525semidirect
520. C2×C4C2×#625semidirect
531. C2×C3#5791semidirect
532. C2×C3#5828semidirect
559. C3C2×#5791semidirect
560. C3C2×#5828semidirect
564. C2#10595022direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×#2352
C23×C3×C4×D32
C2×#641352
C2×#639762
C2×#639612
#105950222
C2×#639082
C2×C4×#6252
C2×#638562
C2×#58283
C2×#57913